The Competing Interactions on a Cayley Tree-Like Lattice: Pentagonal Chandelier

S. Uguza, N. Ganikhodjaevb, H. Akinc and S. Temira aArts and Science Faculty, Department of Mathematics, Harran University, Sanliurfa, 63120, Turkey bDepartment of Computational and Theoretical Sciences, Faculty of Science, IIUM, 25200 Kuantan, Malaysia cFaculty of Education, Department of Mathematics, Zirve University, Gaziantep, 27260, Turkey

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Different types of lattice spin systems with competing interactions have rich and interesting phase diagrams. In this study we present some new results for such systems involving the Ising spin system (i.e. σ = ± 1) using a generalization of the Cayley tree-like lattice approximation. We study the phase diagrams for the Ising model on a Cayley tree-like lattice, a new lattice type called pentagonal chandelier, with competing nearest-neighbor interactions J1, prolonged next-nearest-neighbor interactions Jp and one-level next-nearest-neighbor senary interactions Jl1(6). The colored phase diagrams contain some multicritical Lifshitz points that are at nonzero temperature and many modulated new phases. We also investigate the variation of the wave vector with temperature in the modulated phase and the Lyapunov exponent associated with the trajectory of the system.

DOI: 10.12693/APhysPolA.121.114 PACS numbers: 05.50.+q, 64.60.-i, 64.60.De